Apple boss Tim Cook is furious. How dare Brussels’ meddling competition regulators retrospectively unpick a tax deal that the iPhone-maker had secured from Ireland a quarter of a century ago. What business is it of theirs? Tax, after all, is a sovereign issue for each individual member state within the European Union. The European commission’s ruling would have a “profound and harmful effect” on investment and job creation in Europe, he said.

His political allies at home have waded in too. US Treasury secretary Jack Lew warned last week that the move could have a “chilling effect on US-EU cross-border investment”. The US would have to “consider potential responses”.

According to the Cook script, Apple is a good corporate citizen with a long history of investment and employment in Ireland. That is why, quite properly, almost two-third’s of the group’s profits arise in its Irish-registered subsidiaries. On Tuesday, he posted a lengthy message direct to customers explaining what a travesty of justice Brussels’ intervention had been, with “no basis in fact or in law”.

That, of course, is hogwash. Whatever you think of the commission’s intervention, any honest discussion of Apple’s taxes must start with the admission that its subsidiaries in Knocknaheeny, a run-down suburb of Cork, do not produce almost two-thirds of the group’s profits.

That Cook still clings to this narrative is disappointing, and does not reflect well on those advisers he has gathered around him.

The Apple CEO would do well to listen a little to the candid reflections of the firm’s co-founder Steve Wozniak. Earlier this year, he said: “I don’t like the idea that Apple might be unfair – not paying taxes the way I do as a person.”

For all that, Wozniak noted, on the other hand there are always commercial pressures at play. “Any company that is a public company, its shareholders are going to force it to be as profitable as possible. And that means financial people studying all the laws of the world and figuring out all the schemes that work that are technically legal.”

Cook, though, has his own, cleaner, less equivocal, version of events. And Tuesday was not the first time he has taken to the stage, with faux exasperation, offering justifications of Apple’s huge Irish profits that have for years gone almost entirely untaxed. In 2013, he appeared before the US senate subcommittee on investigations to reject a detailed analysis of the group’s tax planning from Carl Levin (Democrat) and John McCain (Republican).

“You shifted that golden goose to Ireland,” Levin accused Cook, summing up his verdict during a six-hour hearing. “You shifted it to three companies that do not pay taxes in Ireland … These are the crown jewels of Apple Inc … Folks, it’s not right.”

Cook affected incredulity. “There is no [profit] shifting going on that I see at all,” he said. “Apple has real operations in real places, with Apple employees selling real products to real customers. We pay all the taxes we owe – every single dollar … We don’t depend on tax gimmicks.”

That message is now as obsolete as an iPod Classic. Nevertheless, sorting out a fair resolution of Apple’s tax affairs remains less obvious. Where exactly has the tech firm be avoiding its dues? If not Ireland, then where are Apple’s profits truly made?

The fact that the group’s tax structure has been subject to fierce attack from critics in both Washington and Brussels shows that there are several parties who feel they are entitled to spoils from any revised tax settlement.

At present though, it is Ireland that is set to benefit from the European commission’s decision. And the result could be a one of the largest ever bills for back taxes, running into many billions of euros. Brussels officials have suggested the figure could be up to €13bn (£11bn), though the final sum will be for the Irish tax office to determine.

Add to that sum interest charges stretching back more than 10 years and the final tally could put a modest, but not insignificant, dent in Apple’s colossal offshore reserves. At last count, this cash pile stood at more than $200bn (£152bn).

However dim the view you take of Apple’s tax planning, though, a multibillion euro windfall for Ireland looks perverse. Critics on both sides of the Atlantic have castigated Dublin’s politicians and regulators for helping Apple spirit taxable profits away from other jurisdictions. Why should Irish taxpayers end up winners?

It is an uncomfortable irony that Margrethe Vestager, Europe’s competition commissioner, is well aware of. After announcing her Apple decision, she stressed that it was now open to other countries to draw on the commission’s analysis and make their own sub-claims on Apple’s Irish back taxes. Even America, she appeared to hint, could have a call on this money.

All of which looks a messy prospect, which is unlikely to be resolved for many years. As Vestager noted, her powers are limited. Occasional moves by Brussels to police the taxation of multinationals need to be complemented by co-ordinated and sustained international efforts that close loopholes and ensure tax regimes keep pace with the digital economy.

Some argue that Vestager did more on Tuesday to damage than to assist this fragile international consensus on tackling tax avoidance. Certainly her intervention has ruffled feathers and, in the short term at least, appears to offer a far from perfect resolution.

That said, any serious effort to root out toxic tax behaviour is bound to create upset along the way. There are powerful vested interests that would like to see the taxation of corporate profits wither and fade into history. Vestager has set herself against such ambitions. A few more politicians showing her courage would be a fine thing.